Scaling Theory For Subnormal Collective Modes Of A Spherically Symmetric Two-component Bose-einstein Condensate

In recent years,the researches on the problem of two-component and more than two-component Bose-Einstein condensation have gradually deepen,and become a hot topic in the study of Condensed Matter Physics.It is not easy to study separately the nature of a particle and the interaction law between each particle,which requires the introduction of the concept of collective excitation,the collective excitation of Bose-Einstein condensation(BEC)as a fundamental problem for many body problem research is obviously very important.Methods of describing collective excitation include: method of solving Bogoliubov de gennes(Bdg)equations,variational method,scaling theory method,Thomas-Fermi(TF)approximation method,etc.By using the scaling theory and completely analytical method,the modes of collective excitation of two-component Bose-Einstein condensation(2BEC)are studied in this paper.Up to now,there is no work on 2BEC by using the scaling theory.In general,the method of combining analytical and numerical simulation is using for such complex problems like multi-component BEC.The concise but difficult completely analytical method is using in this paper.Firstly,the hydrodynamic equations in the TF approximation are brought up from the coupled Gross-Pitaevskii(CGP)equations describing the dynamic characteristics of 2BEC,the hydrodynamic equations in the TF approximation under the scaling theory are derived,and the equations for solving the low energy excitation modes of axisymmetric 2BEC are derived.Then,the analytical expression for the frequencies and amplitudes of high and low monopole modes in spherically symmetric 2BEC are solved,including the analytical expressions of the coupled coefficient describing the interaction between the two components as well as other interrelated physical quantity.Finally,the analytical expressions are nondimensionalized,and the coupled interactional strength dependence of the frequencies and the two-component mixing degree of high and low monopole modes are investigated by calculation.